8a_Hypothesis_Testing_Outline_Slides

8a_Hypothesis_Testing_Outline_Slides - Glasses and IQ...

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Hypothesis Testing Are people who wear glasses more intelligent than normal? Glasses and IQ Measure the IQ of 1 randomly selected person who wears glasses. 52 68 84 100 116 132 48 Glasses and IQ -3 -2 -1 0 1 2 3 112 Raw IQ scores Problems? • Larger sample should be more accurate 52 68 84 100 116 132 48 Glasses and IQ -3 -2 -1 0 1 2 3 Raw IQ scores 112

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Problems? • The person might simply be normal – Normal people can have an IQ that high 52 68 84 100 116 132 48 Glasses and IQ -3 -2 -1 0 1 2 3 Raw IQ scores 112 In fact, the probability of randomly choosing a normal person with an IQ above 111 is .2451 52 68 84 100 116 132 48 Glasses and IQ -3 -2 -1 0 1 2 3 Raw IQ scores 112 Again, with n = 30 But, those 30 people might still just be normal and they could have a mean IQ of 109 52 68 84 100 116 132 48 Glasses and IQ -3 -2 -1 0 1 2 3 Raw IQ scores M = 109 Again, with n = 30 In fact, the probability of a randomly drawn group of 30 having an IQ above 108 is .0031 -3 -2 -1 0 1 2 3 when n = 30 σ M = 2.92 Sampling distribution of the mean for n = 30 52 68 84 100 116 132 48 Glasses and IQ M = 109
The fundamental problem: There’s always some chance that our sample looks different from the regular population but it really isn’t Because you can still draw individuals and groups from the regular population and find means that are different from the population mean ( sampling error ) Glasses and IQ So we can never be 100% sure that people who wear glasses are smarter than average BUT When the probability of getting our sample mean from the regular population by chance is low, we can be fairly confident that the people in our sample are in fact different from the regular population — in other words, they’re part of their own population Glasses and IQ Essential Problem We want to know if some group of scores is different from another group of scores. But because of variability in populations, and sampling error, we need to guard against the possibility that differences between groups are merely due to chance — to guard against differences that aren’t really genuine. Essential Problem It’s possible that the difference we suspect does not exist. It’s possible that the manipulation that we introduced had no effect.

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Essential Problem So we hope to find a difference that is unlikely to merely be the result of chance In which case, we have confidence that the difference is genuine Hypothesis Testing Hypothesis test — A statistical method that uses sample data to evaluate a hypothesis about a population Hypothesis Testing 4 Steps 1. Formally state hypotheses 2. Set decision criteria 3. Take sample and calculate statistics 4. Make a decision (as dictated by 1-3) Illustrative Example SAT scores µ = 500 σ = 100 Do students who are frequently on Facebook perform differently on the SATs?
Two opposing hypotheses: • Hypothesis A — the population of interest is not different from the general population • Facebook has no effect on SAT scores • called the

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This note was uploaded on 08/22/2011 for the course PSY 207 taught by Professor Pfordesher during the Fall '07 term at SUNY Buffalo.

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8a_Hypothesis_Testing_Outline_Slides - Glasses and IQ...

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